Time in QFT and in special relativity

Special relativity gives that time for a (traveler on) photon do not run. It also gives that every moving elementary particle rest in some inertial system, but photon does not rest in any inertial system.

But how this can be visible in Quantum field theory or in QED? An electron and a photon are too similar in QED.

Special relativity gives that time for a (traveler on) photon do not run. It also gives that every moving elementary particle rest in some inertial system, but photon does not rest in any inertial system.

But how this can be visible in Quantum field theory or in QED? An electron and a photon are too similar in QED.

If photons have no mass then why do we treat them as particles?
A photon probably is a form of energy, not a particle.
The best we can do is give it a theoretical mass as

Energy equivalent of photon mass = m(photon) = hf/(c2).
Will it then run into trouble with Relativity?

Photons have zero invariant mass. In modern textbooks, both massive and massless fields are constructed as representations of the Poincare group. The older terminology of "particle" is gradually being replaced by "field".

A photon probably is a form of energy, not a particle.

It's misleading to say that a photon "is" a form of energy. A more accurate picture is that a photon field has both energy and momentum.

The best we can do is give it a theoretical mass as
Energy equivalent of photon mass = m(photon) = hf/(c2).
Will it then run into trouble with Relativity?

What you describe is called the "relativistic mass", which is a distinct concept from "invariant mass". (Both can be useful in different circumstances.)

Relativistic mass changes under velocity boost transformations. But invariant mass is (surprise!) invariant under those transformations.

It does, but not in a Lorentz inertial system. It is at rest in a light-cone inertial system. The coordinate transformation from Lorentz coordinates x, t to light-cone coordinates x', t' is
x'=x-ct
t'=x+ct